The tree property at the double successor of a singular cardinal with a larger gap

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F18%3A10325737" target="_blank" >RIV/00216208:11210/18:10325737 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.apal.2018.02.002" target="_blank" >https://doi.org/10.1016/j.apal.2018.02.002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apal.2018.02.002" target="_blank" >10.1016/j.apal.2018.02.002</a>

Result language
angličtina
Original language name
The tree property at the double successor of a singular cardinal with a larger gap
Original language description
Starting from a Laver-indestructible supercompact $kappa$ and a weakly compact $lambda$ above $kappa$, we show there is a forcing extension where $kappa$ is a strong limit singular cardinal with cofinality $omega$, $2^kappa = kappa^{+3} = lambda^+$, and the tree property holds at $kappa^{++} = lambda$. Next we generalize this result to an arbitrary cardinal $mu$ such that $kappa <cf{mu}$ and $lambda^+ le mu$. This result provides more information about possible relationships between the tree property and the continuum function.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF15-34700L" target="_blank" >GF15-34700L: The continuum, forcing and large cardinals</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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